OCR C1 — Question 9

Exam BoardOCR
ModuleC1 (Core Mathematics 1)
TopicStraight Lines & Coordinate Geometry

9.
\includegraphics[max width=\textwidth, alt={}, center]{6dc260d0-efec-42b8-995f-5a9e1b964255-3_659_1109_251_404} The diagram shows the parallelogram \(A B C D\).
The points \(A\) and \(B\) have coordinates \(( - 1,3 )\) and \(( 3,4 )\) respectively and lie on the straight line \(l _ { 1 }\).
  1. Find an equation for \(l _ { 1 }\), giving your answer in the form \(a x + b y + c = 0\), where \(a , b\) and \(c\) are integers. The points \(C\) and \(D\) lie on the straight line \(l _ { 2 }\) which has the equation \(x - 4 y - 21 = 0\).
  2. Show that the distance between \(l _ { 1 }\) and \(l _ { 2 }\) is \(k \sqrt { 17 }\), where \(k\) is an integer to be found.
  3. Find the area of parallelogram \(A B C D\).